Question

Show that the energy required to build up the current \( I \) in a coil of inductance \( L \) is \( \frac{1}{2} L I^2 \).

Hint:

The energy stored in an inductor is \( \frac{1}{2} L I^2 \), which represents the work done in establishing the magnetic field.

Answer 1

The energy required to establish a current \( I \) in an inductor is given by the work done in establishing the magnetic field within the inductor. The power delivered to the coil is: \[ P = V I = L \frac{dI}{dt} I \] The total energy is the integral of power over time: \[ W = \int_0^I L I' dI' = \frac{1}{2} L I^2 \] Thus, the energy required to build up the current \( I \) in the coil is \( \frac{1}{2} L I^2 \).